Numerators and Denominators in AdditionDate: 3/3/96 at 9:46:30 From: "David P. Lovett" Subject: adding fractions Why do we add numerators but not denominators when we add fractions with like denominators? Date: 3/4/96 at 21:55:45 From: Doctor Ken Subject: Re: adding fractions Hello! The answer to your question can actually be seen by looking at the English language, of all things! Let's say we have 3 oranges, and we add that to 5 oranges. What do we get? We get 8 oranges. We DON'T get 8 (oranges+oranges). That would be pretty weird. Well, the situation is just the same with fractions. If we're adding 3/11 + 5/11, we're not adding oranges any more, we're adding these things called "elevenths." This fact is reflected in how we say this sentence:"3 elevenths plus 5 elevenths equals 8 elevenths."If we replace "elevenths" with "oranges," we get the same kind of thing: "3 oranges plus 5 oranges equals 8 oranges." So that's why. Here's a question for you: why do we need a common denominator in the first place? -Doctor Ken, The Math Forum |
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